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Analysis of porous filled heat exchangers for electronic cooling
International Journal of Heat and Mass Transfer 133 (2019) 268–276
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Analysis of porous filled heat exchangers for electronic cooling Carlos Zing a, Shadi Mahjoob a, Kambiz Vafai b,⇑ a b
California State University, Northridge, CA, USA University of California, Riverside, CA, USA
a r t i c l e
i n f o
Article history: Received 12 July 2018 Received in revised form 9 December 2018 Accepted 10 December 2018
a b s t r a c t An innovative porous filled heat exchanger is modeled to investigate the cooling effectiveness and temperature distribution at its base subject to a high heat flux. The effects of different nanofluid coolants (5% titanium dioxide (TiO2) in water, 1% alumina in water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 1% diamond in 40:60 ethylene glycol/water), different porous materials (copper and annealed pyrolytic graphite (APG)), and porosity values are investigated. The coolant enters from an inlet channel normal to the base, moves through the porous medium, and leaves the heat exchanger through two opposite exit channels parallel to the base. The effects of the inclination angle of the foam filled channel, inlet velocity value, and heat flux value are also studied. In addition, the effect of the inlet cross section is investigated by studying two different designs. One of the designs has a rectangular cross sectional inlet channel (extended all along the transverse direction) and the other design has a square one. The results indicate the importance of the utilization of a high conductive porous material. Utilization of APG porous matrix improves the cooling effectiveness at the base of the heat exchanger, for all studied coolants of pure water and water based nanofluids. The results also show that utilizing titanium dioxide nanofluids (TiO2) as coolant for both copper and APG porous matrices at low and high porosity structures, and for both square and rectangular inlet cross sections improves the cooling efficiency and temperature uniformity over the base. Investigation of the effect of inlet channel geometry, i.e., square and rectangular, indicates that employing a square cross section inlet channel would result in lower temperature values along the streamwise direction while higher temperature values are observed far from the center in transverse direction. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction The high amount of heat production in electronics systems threatens the safety of its components and increases the failure rate. As such, cooling techniques have a key role in keeping the temperature of electronics devices, such as processors, memory, and graphics chips, below a maximum operating temperature. The demand for smaller electronics components and higher processing speeds will continuously increase the heat flux value and the temperature in electronic components. As such, these components may break down when operating for long periods of time at high temperatures, and the failure rate increases almost at an exponential rate with the operating temperature [1]. Some of the main heat transfer methods to extract heat from electronic components include indirect liquid cooling, natural convection plus radiation, forced air convection, and immersion cooling. It is shown that utilization of porous inserts can improve cooling effectiveness and temperature control [2]. The porous substrate provides a very ⇑ Corresponding author. E-mail address: [email protected] (K. Vafai). https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.067 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
large surface area for a given volume that is a key parameter in the heat transfer process. Metal foam is a porous material in which an interconnected system of metal filaments provides a light and highly conductive substrate. At its basic level, usually each pore is made of a polyhedron with 12–14 faces with each face being a pentagon or hexagon. The foam can be described by its porosity, pore diameter, filament thickness, pore density, and permeability. A reduction in pore size or porosity or an increase in pore density results in higher heat transfer and pressure drop. Based on the application, a compromise between the heat transfer rate and pressure drop should be done [2]. Hwang et al. [3] experimentally investigated the effects of porosity and Reynolds number on the interstitial convection heat transfer coefficient and friction factor for an aluminum foam. Their results indicate that by lowering the porosity while keeping a constant Reynolds number, the interstitial convection coefficient and pressure loss would increase. In addition, by increasing the Reynolds number and holding the porosity constant, both the convection coefficient and change in pressure would increase. An analytical study by Zhao et al. [4] also confirmed these findings
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Nomenclature c df Da F h k keff K L P q qw t T u ! v x X y z Z
specific heat filament diameter Darcy number geometric function convective heat transfer coefficient thermal conductivity effective thermal conductivity permeability length of the base (Fig. 1) pressure heat flux wall heat flux maximum thickness of the porous substrate temperature velocity velocity vector horizontal streamwise direction non-dimensional position along the streamwise direction, 2x/L vertical coordinate horizontal transverse direction non-dimensional position along the transverse direction, 2z/L
regarding the effect of porosity. More details can be found in [2,5– 7]. Utilization of nanofluids may improve heat transfer and thermal efficiencies [8,9]. A nanoparticle is an aggregation of 100–1000 s of atoms, making them orders of magnitude smaller than the channels found in microchannels, making it less probable for a clot to form. In addition, because of its small size, a small momentum is generated with little chance of causing erosion. Khanafer and Vafai [9] presented an extensive critical synthesis of thermophysical characteristic models for nanofluids, mapping properties for different nanofluids at different temperatures and concentrations for various particle sizes. In this work, an innovative porous filled heat exchanger is numerically modeled to study the thermal effectiveness for different nanofluid coolants, porous materials, and porosity values. The heat exchanger design employs a jet impingement technique and its geometrical design is investigated utilizing two types of rectangular and square cross section inlet channels. Although the utilization of conductive porous materials, jet impingement cooling techniques and nanofluid coolants have been previously studied for heat transfer augmentation in literature, this work represents a compact heat exchanger that can employ all these features for cooling of electronic devices subject to very high heat flux values. This presented heat exchanger can have several applications, including but not limited to, electronics cooling and cooling of biomedical devices, and solar radiation receivers [10,11].
Greek symbols inclination angle porosity density dynamic viscosity hw non-dimensional base temperature, t kinematic viscosity K inertia parameter
a e q l
kcopper ðTw Tin Þ qw t
Subscripts in inlet f fluid out outlet s solid w base surface wall 1 free stream Symbol hi
‘‘local volume average” of a quantity
exit channels. The base of the heat exchanger, with a size of 5.25 5.25 cm2, is subject to a uniform heat flux of 106 W/m2. The thickness of inlet and exit channels are 33% and 4.8% of the length of the porous substrate at the base ((L = 5.25 cm) in Fig. 1), respectively. The maximum thickness of the porous substrate is 0.13 L which reduces to 0.048 L at the exit. Most of the sizes are selected based on an earlier optimization study [7]. Except for the base, all other walls are assumed to be insulated. Flow enters the heat exchanger at a temperature of 300 K with a uniform velocity of 4 cm/s for the cases with rectangular cross section and 12.12 cm/s for the cases with square cross section to provide similar flow rates for all cases. The flow is considered to be fully developed before reaching the porous substrate. Some of the represented data and discussions will focus on the streamwise and transverse centerlines. The streamwise centerline is the base line towards the exit (along the x axis), and the transverse centerline is the base line perpendicular to the streamwise line (along the z axis). In addition to water, four different nanofluid coolants are studied namely; 1% alumina in water, 1% diamond in 40:60 ethylene glycol/water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 5% titanium dioxide (TiO2) in water. The coolants will be treated as homogenous fluids with Newtonian behavior whose effective properties are presented in Table 1 [9,12–18]. Two different porous solid materials, copper [19] and annealed pyrolytic graphite (APG) [20,21], are studied (Table 2) with constant pore filament thickness of 4.3154 104 m for porosity values of 0.45 and 0.9.
2. Innovative heat exchanger set up 3. Governing equations Typically, the porous filled heat exchanger can be attached to the surface of the electronic device to be cooled and is subjected to a high heat flux leaving the device. A schematic diagram of the heat exchanger is presented in Fig. 1. Two different inlet channels are investigated; one for a rectangular cross section (extended all along transverse direction) and the other one for a square cross section (Fig. 1b and c). The working fluid enters through a vertical channel, passes through the porous substrate and leaves through two similar lateral
Two different regions will be analyzed in this system; the porous substrate and the entrance/exit channels. 3.1. Inlet-exit channels The employed governing equations (for continuity, momentum, and energy) for steady state, incompressible, and laminar flow inside the entrance and exit channels are
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Fig. 1. Schematic of the investigated geometries (a) the front view (streamwise direction) (b) the case with rectangular cross sectional inlet channel (c) the case with square cross sectional inlet channel.
Table 1 Effective properties of the investigated coolants [9,12–18].
Water 1% alumina in water 1% diamond in 40:60 ethylene glycol/water 0.03% multi walled carbon nanotubes (MWCNT) in water 5% titanium dioxide in water
q
(kg/m3)
c (J/kg K)
k (W/m K)
l
998.2 1025 1080.1 998.7 1157
4182 4063 3438.4 4181 4007.5
0.6 0.63 0.4467 0.685 0.774
0.001003 0.001028 0.00494 0.000874 0.001394
Table 2 Properties of the investigated porous materials [19–21].
Copper APG
q
(kg/m3)
c (J/kg K)
k (W/m K)
8978 2260
381 702
387.6 1700
qf D! !E l D!E l D!E v r v ¼ rhPi f þ r2 v v e e K h D D E i qf F e ! ! pffiffiffiffi K
vi
D E qf cf ! v rhT i ¼ keff r2 hT i
v
J
(kg/m s)
ð5Þ ð6Þ
where [2,7],
r! v ¼0
ð1Þ
keff ¼ ekf þ ð1 eÞks
ð7Þ
! ! qf ! v r v ¼ rP þ lr2 v
ð2Þ
qf cf ! v rT ¼ kf r2 T
1:75 F ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi 150e3
ð8Þ
ð3Þ K¼
3.2. Porous substrate
e3 d2f 150ð1 eÞ2
ð9Þ
For the porous region of the system, the steady state, volume averaged governing equations are [22]
4. Computational methodology
r ! v ¼0
For numerical modeling, utilizing ANSYS FLUENT, an implicit, segregated, pressure-based, control volume method is employed
D E
ð4Þ
C. Zing et al. / International Journal of Heat and Mass Transfer 133 (2019) 268–276
to solve the coupled, non-linear governing equations. Integrating the equations over each cell in the grid, the equations are discretized, turning the nonlinear equations linear. The gradients are evaluated using the Least Squares Cell Based method, assuming the cell centered scalar varies linearly with the neighboring cells. All diffusive terms, including the cell face pressure, are set to be discretized using a central differencing scheme. For the momentum and energy convective terms, a second order upwind scheme is applied. The SIMPLE pressure-based segregated algorithm is used to solve the system. The SIMPLE algorithm will iterate until every scalar’s globally scaled residual reaches a minimum of 106, as the convergence criteria. Each system of equations is solved using the Gauss-Seidel iterative method with the help of the Algebraic Multigrid (AMG) scheme in order to increase accuracy and the convergence speed [19]. 4.1. Code validation study To validate the numerical modeling and the results, the velocity and temperature profiles are validated against those of analytical solution by Vafai and Kim [23], for a fully developed flow through a porous filled parallel-plate channel, subject to a uniform heat flux from both plates. The comparisons are performed for two different values of inertia parameters (K) at a Darcy number of Da1/2 = 10, defined as [23]
Da ¼
1 K H
2
ð10Þ
e
K ¼ e3=2 F
u1 H
mf
ð11Þ
271
where 2H indicates the channel height. The comparison of the results indicates an excellent agreement for velocity and temperature profiles for different inertia parameters (Fig. 2). 4.2. Grid resolution study A multi-block structured quadrilateral grid is utilized for grid generation while mesh sizes are set to be finer within the porous region and near the wall boundaries to properly capture flow field characteristics. In order to study grid independence of the results, several grid sizes are examined. As an example, the nondimensional temperature distributions along the streamwise centerline of the investigated heat exchanger, with rectangular and square cross sectional inlets and a porosity of 0.45, are presented for different grid sizes in Fig. 3. It can be seen that a gird resolution composed of 613,000 cells (for rectangular cross section) and 1,032,000 cells (for square cross section) result in a grid independent solution while properly capturing the flow field characteristics. Varying the imposed heat flux led to the same conclusion regarding the adequate number of cells for a grid independent solution. 5. Results Porous filled heat exchangers with rectangular and square cross section inlet channels are investigated. The effect of inclination angle, heat flux, coolant velocity, porous material, porosity value and multiple nanofluid coolants are studied. The heat exchanger design employs inclined walls to improve temperature uniformity along the base subject to a high heat flux value. The importance of
Fig. 2. Comparison of the non-dimensional velocity and temperature profiles in a porous filled channel with those of an analytical solution by Vafai and Kim [23] at Da1/ = 10 and K = 10, 100 (a) non-dimensional velocity (b) non-dimensional temperature.
2
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Fig. 3. Non-dimensional temperature profile comparisons for grid independence study of the investigated geometries with a porosity of 0.45 for (a) rectangular and (b) square cross sectional inlet channels, subject to a uniform heat flux of 106 W/m2.
Fig. 4. Non-dimensional temperature distribution along the streamwise direction on the base centerline of the cases with the inclination angles of 5.96° and 13.74° and parallel channel walls.
Fig. 5. Non-dimensional temperature distribution along the streamwise direction on the base centerline for different inlet velocities.
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the channel inclined walls is investigated in Fig. 4. The streamwise non-dimensional temperature at the centerline of the base surface of four different copper porous filled heat exchanger designs are compared. The porosity of the copper is 0.45 and all designs are subject to a uniform heat flux of 106 W/m2 and employ rectangular cross section inlet. Two designs employ inclined walls; one with an inclination angle of 5.96° and the other one with an angle of 13.74°. As such, the thickness of the porous filled channels varies between 0.13 L and 0.095 L for the inclination angle of 5.96° and between 0.13 L and 0.048 L for the inclination angle of 13.74°. The other two designs employ parallel channels; i.e. zero inclination angle, whose thicknesses are the same as the maximum and minimum thickness of the investigated counterpart cases with inclined walls (0.13 L and 0.048 L). As the results indicate, the cases with inclined walls provide a considerably more uniform temperature distribution. Decreasing the channel thickness, without utilizing the inclined walls, may result in lower temperature at some locations but larger temperature non-uniformity would be obtained (Fig. 4). As such, a heat exchanger with an inclination angle of 13.74° is selected in this study providing low temperature values and most temperature uniformity along the base centerline. In many cooling applications, the goal is to provide a uniform temperature at the surface while keeping the surface at low temperature. The effect of inlet velocity value on the temperature distribution on the base is also investigated for a copper foam filled heat exchanger with rectangular cross sectional inlet and porosity of 0.45 which is subject to a uniform heat flux of 106 W/m2 for the same coolant temperature of 300 K (Fig. 5). An increase in the velocity, and so mass flow rate, will result in lower and more uniform temperature distribution on the base. However, a higher velocity value will cause a larger pressure drop and so higher
273
required pumping power. To investigate the effect of heat flux in this study, different heat flux values are investigated for a copper foam filled heat exchanger with a porosity of 0.45. The coolant temperature and velocity are set to be 300 K and 4 cm/s, respectively. To better study the temperature distribution on the base, the temperature values are once non-dimensionalized using a fixed value of heat flux (106 W/m2) (Fig. 6a) and once nondimensionalized using the corresponding heat flux (Fig. 6b). As expected, higher heat flux corresponds to a higher surface temperature (Fig. 6a). However, as Fig. 6b indicates, the non-dimensional temperature distribution and uniformity are independent of heat flux value when temperature is non-dimensionalized using the corresponding heat flux value. As such, regardless of the heat flux value, the temperature profiles are similar. The effects of porous materials, namely copper and APG, and porosity value are studied for rectangular and square cross sectional inlet channels (Fig. 7). The results indicate that both copper and APG can properly cool down the base which is subjected to a very high heat flux value. Our investigations confirm the importance of employing the porous substrate in the heat exchanger design to decrease the base temperature below a safe temperature value. Comparing the investigated porous substrates, APG porous substrate can provide a better cooling over the base, for all studied coolants of pure water and water based nanofluids, and for high and low porosity values. APG is a lighter and more conductive material, but fragile in comparison with copper. In addition, as expected, a reduction in porosity improves cooling effectiveness for all studied cases (Fig. 7). As such, the maximum temperature can be reduced by either utilization of a more conductive material or by a reduction in porosity. However, a lower porosity value results in a larger pressure drop and so higher required pumping power.
Fig. 6. Non-dimensional temperature distribution along the streamwise direction on the base centerline for different wall base surface heat flux values. Temperature values are non-dimensionalized using (a) a heat flux value of 106 W/m2 (b) corresponding heat flux.
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Fig. 7. Non-dimensional temperature distribution along the streamwise direction at the base centerline, for rectangular (Rect.) and square (Sq.) cross sectional inlet channels, for different coolants (a) Copper porous insert with a porosity of 45%, (b) APG porous insert with a porosity of 45%, and (c) APG porous insert with a porosity of 90%.
The effect of different nanofluid coolants are also investigated in Fig. 7. The studied nanofluid coolants are 5% titanium dioxide (TiO2) in water, 1% alumina in water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 1% diamond in 40:60 ethylene glycol/water. The results indicate that titanium dioxide (TiO2) nanofluid coolant has more cooling effectiveness compared to other studied coolants (nanofluids and water), for both copper and APG porous matrices for high and low porosity values. Comparing the studied coolants, diamond nanofluid has the lowest thermal effectiveness in comparison with pure water and all other studied water based nanofluid coolants. Investigation of temperature distribution over the base indicates a sinusoidal like behavior with a high temperature peak at the center point of the base, for all the studied cases (Fig. 7). The center peak is due to development of stagnation point at the center
of the base and the fluid’s deceleration as it moves towards that region. On both sides of the stagnation point, more efficient cooling is achieved as such minimum temperature regions are developed. As expected, the highest temperature values are observed near the exit channels for all cases. The effect of the inlet cross section on temperature distribution is also presented in Fig. 7. To better investigate the effect of inlet cross section, the mass flow rate is kept the same at the entrance of both rectangular and square inlets. As such, the entrance velocity for the cases with rectangular cross section is set to be 4 cm/s while it is 12.12 cm/s for the cases with square cross section. The results indicate lower temperature values and therefore an improved cooling effectiveness along the streamwise direction, for all cases with square cross sections compared to those with rectangular cross section. In square cross sectional inlet channel,
C. Zing et al. / International Journal of Heat and Mass Transfer 133 (2019) 268–276
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Fig. 8. Non-dimensional temperature distribution along the transverse direction at the base centerline, for rectangular (Rect.) and square (Sq.) cross sectional inlet channels, for different coolants (a) Copper porous insert with a porosity of 45%, (b) APG porous insert with a porosity of 45%, and (c) APG porous insert with a porosity of 90%.
titanium dioxide (TiO2) nanofluid coolant provides more cooling effectiveness compared to other studied coolants (nanofluids and water), for both copper and APG porous matrices for different porosity values. In summary, similar results are observed regarding the effect of porous material, porosity and nanofluids for both square and rectangular cross section channels. Temperature distribution along the transverse direction at the centerline of the base is also studied and compared for different coolants, porous materials, and porosity values (Fig. 8). The results confirm that titanium dioxide (TiO2) nanofluid coolant has more cooling effectiveness compared to other studied coolants (nanofluids and water), for both copper and APG porous matrices for high and low porosity values. In addition, the diamond nanofluid has the lowest thermal effectiveness compared to pure water and all other studied water based nanofluid cool-
ants. Also similar to the results for the rectangular cross sectional inlet cases, APG porous substrates provides a better cooling along the transverse direction compared to that of copper substrate for the same coolant or porosity. In addition, the lower porosity would result in more efficient cooling along the transverse direction but at a greater pressure drop. Studying the effect of inlet cross section, the results indicate larger temperature nonuniformity along the transverse direction for the cases with a square cross section. In addition, larger temperature values are observed in the regions far from the inlet channel (Fig. 8). As such, the cases with square cross section provide lower temperature values along the streamwise direction while result in less uniformity specially along transverse direction. Utilization of APG or low porosity substrates improves cooling effectiveness along the transverse direction.
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6. Conclusions Electronic cooling is one of the main issues in the development of advanced devices such as electronics and biomedical components. In this work, an innovative porous filled heat exchanger is numerically modeled to investigate the thermal performance of different nanofluid coolants, porous materials, porosity values, and inlet channel geometry. The heat exchanger is filled with a highly conductive porous insert providing a large surface area for a given volume to enhance heat transfer and thermal control. Two different porous solid materials (copper and annealed pyrolytic graphite (APG)) with different porosity values, utilizing different nanofluids (5% titanium dioxide (TiO2) in water, 1% alumina in water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 1% diamond in 40:60 ethylene glycol/water) are investigated. The results indicate the importance of proper selection of the porous medium and the coolant for improving the cooling process. Both copper and APG porous substrates can provide a proper cooling at the base of the heat exchanger with rectangular and square inlet channels. However, utilization of APG porous matrix provides a better cooling at the base leading to lower temperature values. APG is a lighter and more conductive material, but fragile in comparison with copper. The results also show that utilizing titanium dioxide (TiO2) nanofluid as coolant improves cooling efficiency in all cases with rectangular and square cross sectional inlets, copper and APG porous matrices, and low and high porosity values. The effect of inlet channel geometry, square and rectangular, was also investigated. The results indicate a lower temperature distribution along streamwise direction for the cases with square cross sectional inlet, while along the transverse direction higher temperature values are observed far from the center for the square cross section inlet channel.
Conflict of interest There is no conflict of interest. This manuscript has not been submitted to anywhere else.
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[2] S. Mahjoob, K. Vafai, A synthesis of fluid and thermal transport models for metal foam heat exchangers, Int. J. Heat Mass Transf. 51 (15) (2008) 3701– 3711. [3] J.J. Hwang, G.J. Hwang, R.H. Yeh, C.H. Chao, Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams, J. Heat Transfer 124 (1) (2002) 120–129. [4] C.Y. Zhao, W. Lu, S.A. Tassou, Thermal analysis on metal-foam filled heat exchangers. Part II: tube heat exchangers, Int. J. Heat Mass Transf. 49 (15) (2006) 2762–2770. [5] R. Rachedi, S. Chikh, Enhancement of electronic cooling by insertion of foam materials, Heat Mass Transf. 37 (4) (2001) 371–378. [6] K. Boomsma, D. Poulikakos, F. Zwick, Metal foams as compact high performance heat exchangers, Mech. Mater. 35 (12) (2003) 1161–1176. [7] S. Mahjoob, K. Vafai, N.B. Reginald, Rapid microfluidic thermal cycler for polymerase chain reaction nucleic acid amplification, Int. J. Heat Mass Transf. 51 (9) (2008) 2109–2122. [8] S.K. Das, S.U.S. Choi, H.E. Patel, Heat transfer in nanofluids—a review, Heat Transfer Eng. 27 (10) (2006) 3–19. [9] K. Khanafer, K. Vafai, A critical synthesis of thermophysical characteristics of nanofluids, Int. J. Heat Mass Transf. 54 (19) (2011) 4410–4428. [10] P. Wang, K. Vafai, D.Y. Liu, Analysis of radiative effect under local thermal nonequilibrium conditions in porous media-application to a solar air receiver, Numer. Heat Trans., Part A: Appl. 65 (10) (2014) 931–948. [11] E.M.G. Rodrigues, R. Melicio, V.M.F. Mendes, J.P.S. Catalao, Simulation of a solar cell considering single-diode equivalent circuit model, Renew. Energy Power Qual. J. 1 (2011) 369–373. [12] H.A. Mintsa, G. Roy, C.T. Nguyen, D. Doucet, New temperature dependent thermal conductivity data for water-based nanofluids, Int. J. Therm. Sci. 48 (2) (2009) 363–371. [13] L.S. Sundar, M. Singh, A.C.M. Sousa, Enhanced thermal properties of nanodiamond nanofluids, Chem. Phys. Lett. 644 (2016) 99–110. [14] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer 11 (1998) 151– 170. [15] R. Saleh, N. Putra, R.E. Wibowo, W.N. Spetiadi, S.P. Prakoso, Titanium dioxide nanofluids for heat transfer applications, Exp. Therm. Fluid Sci. 52 (2014) 19– 29. [16] A. Albojamal, K. Vafai, Analysis of single phase, discrete and mixture models, in predicting nanofluid transport, Int. J. Heat Mass Transf. 114 (2017) 225–237. [17] J.S.S. Aravind, P. Baskar, T.T. Baby, K.R. Sabareesh, S. Das, S. Ramaprabhu, Investigation of structural stability, dispersion, viscosity, and conductive heat transfer properties of functionalized carbon nanotube based nanofluids, J. Phys. Chem. C 115 (34) (2011) 16737–16744. [18] N. Pradhan, H. Duan, J. Liang, G. Iannacchione, The specific heat and effective thermal conductivity of composites containing single-wall and multi-wall carbon nanotubes, Nanotechnology 20 (24) (2009) 245705. [19] Ansys Fluent 17.1.0, 2016, ‘‘User Guide,” US. [20] Thermacore Thermal Management Solutions. K-CORE. N.p.: Thermacore thermal management solutions, 2013. Web.. [21] M. Montesano, Annealed pyrolytic graphite, Adv. Mater. Process. 164 (6) (2006) 44. [22] K. Vafai, C.L. Tien, Boundary and inertia effects on flow and heat transfer in porous media, Int. J. Heat Mass Transf. 24 (1981) 195–203. [23] K. Vafai, S. Kim, Forced convection in a channel filled with porous medium – an exact solution, ASME J. Heat Trans. 111 (1989) 103–110.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Analysis of porous filled heat exchangers for electronic cooling Carlos Zing a, Shadi Mahjoob a, Kambiz Vafai b,⇑ a b
California State University, Northridge, CA, USA University of California, Riverside, CA, USA
a r t i c l e
i n f o
Article history: Received 12 July 2018 Received in revised form 9 December 2018 Accepted 10 December 2018
a b s t r a c t An innovative porous filled heat exchanger is modeled to investigate the cooling effectiveness and temperature distribution at its base subject to a high heat flux. The effects of different nanofluid coolants (5% titanium dioxide (TiO2) in water, 1% alumina in water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 1% diamond in 40:60 ethylene glycol/water), different porous materials (copper and annealed pyrolytic graphite (APG)), and porosity values are investigated. The coolant enters from an inlet channel normal to the base, moves through the porous medium, and leaves the heat exchanger through two opposite exit channels parallel to the base. The effects of the inclination angle of the foam filled channel, inlet velocity value, and heat flux value are also studied. In addition, the effect of the inlet cross section is investigated by studying two different designs. One of the designs has a rectangular cross sectional inlet channel (extended all along the transverse direction) and the other design has a square one. The results indicate the importance of the utilization of a high conductive porous material. Utilization of APG porous matrix improves the cooling effectiveness at the base of the heat exchanger, for all studied coolants of pure water and water based nanofluids. The results also show that utilizing titanium dioxide nanofluids (TiO2) as coolant for both copper and APG porous matrices at low and high porosity structures, and for both square and rectangular inlet cross sections improves the cooling efficiency and temperature uniformity over the base. Investigation of the effect of inlet channel geometry, i.e., square and rectangular, indicates that employing a square cross section inlet channel would result in lower temperature values along the streamwise direction while higher temperature values are observed far from the center in transverse direction. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction The high amount of heat production in electronics systems threatens the safety of its components and increases the failure rate. As such, cooling techniques have a key role in keeping the temperature of electronics devices, such as processors, memory, and graphics chips, below a maximum operating temperature. The demand for smaller electronics components and higher processing speeds will continuously increase the heat flux value and the temperature in electronic components. As such, these components may break down when operating for long periods of time at high temperatures, and the failure rate increases almost at an exponential rate with the operating temperature [1]. Some of the main heat transfer methods to extract heat from electronic components include indirect liquid cooling, natural convection plus radiation, forced air convection, and immersion cooling. It is shown that utilization of porous inserts can improve cooling effectiveness and temperature control [2]. The porous substrate provides a very ⇑ Corresponding author. E-mail address: [email protected] (K. Vafai). https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.067 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
large surface area for a given volume that is a key parameter in the heat transfer process. Metal foam is a porous material in which an interconnected system of metal filaments provides a light and highly conductive substrate. At its basic level, usually each pore is made of a polyhedron with 12–14 faces with each face being a pentagon or hexagon. The foam can be described by its porosity, pore diameter, filament thickness, pore density, and permeability. A reduction in pore size or porosity or an increase in pore density results in higher heat transfer and pressure drop. Based on the application, a compromise between the heat transfer rate and pressure drop should be done [2]. Hwang et al. [3] experimentally investigated the effects of porosity and Reynolds number on the interstitial convection heat transfer coefficient and friction factor for an aluminum foam. Their results indicate that by lowering the porosity while keeping a constant Reynolds number, the interstitial convection coefficient and pressure loss would increase. In addition, by increasing the Reynolds number and holding the porosity constant, both the convection coefficient and change in pressure would increase. An analytical study by Zhao et al. [4] also confirmed these findings
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Nomenclature c df Da F h k keff K L P q qw t T u ! v x X y z Z
specific heat filament diameter Darcy number geometric function convective heat transfer coefficient thermal conductivity effective thermal conductivity permeability length of the base (Fig. 1) pressure heat flux wall heat flux maximum thickness of the porous substrate temperature velocity velocity vector horizontal streamwise direction non-dimensional position along the streamwise direction, 2x/L vertical coordinate horizontal transverse direction non-dimensional position along the transverse direction, 2z/L
regarding the effect of porosity. More details can be found in [2,5– 7]. Utilization of nanofluids may improve heat transfer and thermal efficiencies [8,9]. A nanoparticle is an aggregation of 100–1000 s of atoms, making them orders of magnitude smaller than the channels found in microchannels, making it less probable for a clot to form. In addition, because of its small size, a small momentum is generated with little chance of causing erosion. Khanafer and Vafai [9] presented an extensive critical synthesis of thermophysical characteristic models for nanofluids, mapping properties for different nanofluids at different temperatures and concentrations for various particle sizes. In this work, an innovative porous filled heat exchanger is numerically modeled to study the thermal effectiveness for different nanofluid coolants, porous materials, and porosity values. The heat exchanger design employs a jet impingement technique and its geometrical design is investigated utilizing two types of rectangular and square cross section inlet channels. Although the utilization of conductive porous materials, jet impingement cooling techniques and nanofluid coolants have been previously studied for heat transfer augmentation in literature, this work represents a compact heat exchanger that can employ all these features for cooling of electronic devices subject to very high heat flux values. This presented heat exchanger can have several applications, including but not limited to, electronics cooling and cooling of biomedical devices, and solar radiation receivers [10,11].
Greek symbols inclination angle porosity density dynamic viscosity hw non-dimensional base temperature, t kinematic viscosity K inertia parameter
a e q l
kcopper ðTw Tin Þ qw t
Subscripts in inlet f fluid out outlet s solid w base surface wall 1 free stream Symbol hi
‘‘local volume average” of a quantity
exit channels. The base of the heat exchanger, with a size of 5.25 5.25 cm2, is subject to a uniform heat flux of 106 W/m2. The thickness of inlet and exit channels are 33% and 4.8% of the length of the porous substrate at the base ((L = 5.25 cm) in Fig. 1), respectively. The maximum thickness of the porous substrate is 0.13 L which reduces to 0.048 L at the exit. Most of the sizes are selected based on an earlier optimization study [7]. Except for the base, all other walls are assumed to be insulated. Flow enters the heat exchanger at a temperature of 300 K with a uniform velocity of 4 cm/s for the cases with rectangular cross section and 12.12 cm/s for the cases with square cross section to provide similar flow rates for all cases. The flow is considered to be fully developed before reaching the porous substrate. Some of the represented data and discussions will focus on the streamwise and transverse centerlines. The streamwise centerline is the base line towards the exit (along the x axis), and the transverse centerline is the base line perpendicular to the streamwise line (along the z axis). In addition to water, four different nanofluid coolants are studied namely; 1% alumina in water, 1% diamond in 40:60 ethylene glycol/water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 5% titanium dioxide (TiO2) in water. The coolants will be treated as homogenous fluids with Newtonian behavior whose effective properties are presented in Table 1 [9,12–18]. Two different porous solid materials, copper [19] and annealed pyrolytic graphite (APG) [20,21], are studied (Table 2) with constant pore filament thickness of 4.3154 104 m for porosity values of 0.45 and 0.9.
2. Innovative heat exchanger set up 3. Governing equations Typically, the porous filled heat exchanger can be attached to the surface of the electronic device to be cooled and is subjected to a high heat flux leaving the device. A schematic diagram of the heat exchanger is presented in Fig. 1. Two different inlet channels are investigated; one for a rectangular cross section (extended all along transverse direction) and the other one for a square cross section (Fig. 1b and c). The working fluid enters through a vertical channel, passes through the porous substrate and leaves through two similar lateral
Two different regions will be analyzed in this system; the porous substrate and the entrance/exit channels. 3.1. Inlet-exit channels The employed governing equations (for continuity, momentum, and energy) for steady state, incompressible, and laminar flow inside the entrance and exit channels are
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Fig. 1. Schematic of the investigated geometries (a) the front view (streamwise direction) (b) the case with rectangular cross sectional inlet channel (c) the case with square cross sectional inlet channel.
Table 1 Effective properties of the investigated coolants [9,12–18].
Water 1% alumina in water 1% diamond in 40:60 ethylene glycol/water 0.03% multi walled carbon nanotubes (MWCNT) in water 5% titanium dioxide in water
q
(kg/m3)
c (J/kg K)
k (W/m K)
l
998.2 1025 1080.1 998.7 1157
4182 4063 3438.4 4181 4007.5
0.6 0.63 0.4467 0.685 0.774
0.001003 0.001028 0.00494 0.000874 0.001394
Table 2 Properties of the investigated porous materials [19–21].
Copper APG
q
(kg/m3)
c (J/kg K)
k (W/m K)
8978 2260
381 702
387.6 1700
qf D! !E l D!E l D!E v r v ¼ rhPi f þ r2 v v e e K h D D E i qf F e ! ! pffiffiffiffi K
vi
D E qf cf ! v rhT i ¼ keff r2 hT i
v
J
(kg/m s)
ð5Þ ð6Þ
where [2,7],
r! v ¼0
ð1Þ
keff ¼ ekf þ ð1 eÞks
ð7Þ
! ! qf ! v r v ¼ rP þ lr2 v
ð2Þ
qf cf ! v rT ¼ kf r2 T
1:75 F ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi 150e3
ð8Þ
ð3Þ K¼
3.2. Porous substrate
e3 d2f 150ð1 eÞ2
ð9Þ
For the porous region of the system, the steady state, volume averaged governing equations are [22]
4. Computational methodology
r ! v ¼0
For numerical modeling, utilizing ANSYS FLUENT, an implicit, segregated, pressure-based, control volume method is employed
D E
ð4Þ
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to solve the coupled, non-linear governing equations. Integrating the equations over each cell in the grid, the equations are discretized, turning the nonlinear equations linear. The gradients are evaluated using the Least Squares Cell Based method, assuming the cell centered scalar varies linearly with the neighboring cells. All diffusive terms, including the cell face pressure, are set to be discretized using a central differencing scheme. For the momentum and energy convective terms, a second order upwind scheme is applied. The SIMPLE pressure-based segregated algorithm is used to solve the system. The SIMPLE algorithm will iterate until every scalar’s globally scaled residual reaches a minimum of 106, as the convergence criteria. Each system of equations is solved using the Gauss-Seidel iterative method with the help of the Algebraic Multigrid (AMG) scheme in order to increase accuracy and the convergence speed [19]. 4.1. Code validation study To validate the numerical modeling and the results, the velocity and temperature profiles are validated against those of analytical solution by Vafai and Kim [23], for a fully developed flow through a porous filled parallel-plate channel, subject to a uniform heat flux from both plates. The comparisons are performed for two different values of inertia parameters (K) at a Darcy number of Da1/2 = 10, defined as [23]
Da ¼
1 K H
2
ð10Þ
e
K ¼ e3=2 F
u1 H
mf
ð11Þ
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where 2H indicates the channel height. The comparison of the results indicates an excellent agreement for velocity and temperature profiles for different inertia parameters (Fig. 2). 4.2. Grid resolution study A multi-block structured quadrilateral grid is utilized for grid generation while mesh sizes are set to be finer within the porous region and near the wall boundaries to properly capture flow field characteristics. In order to study grid independence of the results, several grid sizes are examined. As an example, the nondimensional temperature distributions along the streamwise centerline of the investigated heat exchanger, with rectangular and square cross sectional inlets and a porosity of 0.45, are presented for different grid sizes in Fig. 3. It can be seen that a gird resolution composed of 613,000 cells (for rectangular cross section) and 1,032,000 cells (for square cross section) result in a grid independent solution while properly capturing the flow field characteristics. Varying the imposed heat flux led to the same conclusion regarding the adequate number of cells for a grid independent solution. 5. Results Porous filled heat exchangers with rectangular and square cross section inlet channels are investigated. The effect of inclination angle, heat flux, coolant velocity, porous material, porosity value and multiple nanofluid coolants are studied. The heat exchanger design employs inclined walls to improve temperature uniformity along the base subject to a high heat flux value. The importance of
Fig. 2. Comparison of the non-dimensional velocity and temperature profiles in a porous filled channel with those of an analytical solution by Vafai and Kim [23] at Da1/ = 10 and K = 10, 100 (a) non-dimensional velocity (b) non-dimensional temperature.
2
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Fig. 3. Non-dimensional temperature profile comparisons for grid independence study of the investigated geometries with a porosity of 0.45 for (a) rectangular and (b) square cross sectional inlet channels, subject to a uniform heat flux of 106 W/m2.
Fig. 4. Non-dimensional temperature distribution along the streamwise direction on the base centerline of the cases with the inclination angles of 5.96° and 13.74° and parallel channel walls.
Fig. 5. Non-dimensional temperature distribution along the streamwise direction on the base centerline for different inlet velocities.
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the channel inclined walls is investigated in Fig. 4. The streamwise non-dimensional temperature at the centerline of the base surface of four different copper porous filled heat exchanger designs are compared. The porosity of the copper is 0.45 and all designs are subject to a uniform heat flux of 106 W/m2 and employ rectangular cross section inlet. Two designs employ inclined walls; one with an inclination angle of 5.96° and the other one with an angle of 13.74°. As such, the thickness of the porous filled channels varies between 0.13 L and 0.095 L for the inclination angle of 5.96° and between 0.13 L and 0.048 L for the inclination angle of 13.74°. The other two designs employ parallel channels; i.e. zero inclination angle, whose thicknesses are the same as the maximum and minimum thickness of the investigated counterpart cases with inclined walls (0.13 L and 0.048 L). As the results indicate, the cases with inclined walls provide a considerably more uniform temperature distribution. Decreasing the channel thickness, without utilizing the inclined walls, may result in lower temperature at some locations but larger temperature non-uniformity would be obtained (Fig. 4). As such, a heat exchanger with an inclination angle of 13.74° is selected in this study providing low temperature values and most temperature uniformity along the base centerline. In many cooling applications, the goal is to provide a uniform temperature at the surface while keeping the surface at low temperature. The effect of inlet velocity value on the temperature distribution on the base is also investigated for a copper foam filled heat exchanger with rectangular cross sectional inlet and porosity of 0.45 which is subject to a uniform heat flux of 106 W/m2 for the same coolant temperature of 300 K (Fig. 5). An increase in the velocity, and so mass flow rate, will result in lower and more uniform temperature distribution on the base. However, a higher velocity value will cause a larger pressure drop and so higher
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required pumping power. To investigate the effect of heat flux in this study, different heat flux values are investigated for a copper foam filled heat exchanger with a porosity of 0.45. The coolant temperature and velocity are set to be 300 K and 4 cm/s, respectively. To better study the temperature distribution on the base, the temperature values are once non-dimensionalized using a fixed value of heat flux (106 W/m2) (Fig. 6a) and once nondimensionalized using the corresponding heat flux (Fig. 6b). As expected, higher heat flux corresponds to a higher surface temperature (Fig. 6a). However, as Fig. 6b indicates, the non-dimensional temperature distribution and uniformity are independent of heat flux value when temperature is non-dimensionalized using the corresponding heat flux value. As such, regardless of the heat flux value, the temperature profiles are similar. The effects of porous materials, namely copper and APG, and porosity value are studied for rectangular and square cross sectional inlet channels (Fig. 7). The results indicate that both copper and APG can properly cool down the base which is subjected to a very high heat flux value. Our investigations confirm the importance of employing the porous substrate in the heat exchanger design to decrease the base temperature below a safe temperature value. Comparing the investigated porous substrates, APG porous substrate can provide a better cooling over the base, for all studied coolants of pure water and water based nanofluids, and for high and low porosity values. APG is a lighter and more conductive material, but fragile in comparison with copper. In addition, as expected, a reduction in porosity improves cooling effectiveness for all studied cases (Fig. 7). As such, the maximum temperature can be reduced by either utilization of a more conductive material or by a reduction in porosity. However, a lower porosity value results in a larger pressure drop and so higher required pumping power.
Fig. 6. Non-dimensional temperature distribution along the streamwise direction on the base centerline for different wall base surface heat flux values. Temperature values are non-dimensionalized using (a) a heat flux value of 106 W/m2 (b) corresponding heat flux.
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Fig. 7. Non-dimensional temperature distribution along the streamwise direction at the base centerline, for rectangular (Rect.) and square (Sq.) cross sectional inlet channels, for different coolants (a) Copper porous insert with a porosity of 45%, (b) APG porous insert with a porosity of 45%, and (c) APG porous insert with a porosity of 90%.
The effect of different nanofluid coolants are also investigated in Fig. 7. The studied nanofluid coolants are 5% titanium dioxide (TiO2) in water, 1% alumina in water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 1% diamond in 40:60 ethylene glycol/water. The results indicate that titanium dioxide (TiO2) nanofluid coolant has more cooling effectiveness compared to other studied coolants (nanofluids and water), for both copper and APG porous matrices for high and low porosity values. Comparing the studied coolants, diamond nanofluid has the lowest thermal effectiveness in comparison with pure water and all other studied water based nanofluid coolants. Investigation of temperature distribution over the base indicates a sinusoidal like behavior with a high temperature peak at the center point of the base, for all the studied cases (Fig. 7). The center peak is due to development of stagnation point at the center
of the base and the fluid’s deceleration as it moves towards that region. On both sides of the stagnation point, more efficient cooling is achieved as such minimum temperature regions are developed. As expected, the highest temperature values are observed near the exit channels for all cases. The effect of the inlet cross section on temperature distribution is also presented in Fig. 7. To better investigate the effect of inlet cross section, the mass flow rate is kept the same at the entrance of both rectangular and square inlets. As such, the entrance velocity for the cases with rectangular cross section is set to be 4 cm/s while it is 12.12 cm/s for the cases with square cross section. The results indicate lower temperature values and therefore an improved cooling effectiveness along the streamwise direction, for all cases with square cross sections compared to those with rectangular cross section. In square cross sectional inlet channel,
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Fig. 8. Non-dimensional temperature distribution along the transverse direction at the base centerline, for rectangular (Rect.) and square (Sq.) cross sectional inlet channels, for different coolants (a) Copper porous insert with a porosity of 45%, (b) APG porous insert with a porosity of 45%, and (c) APG porous insert with a porosity of 90%.
titanium dioxide (TiO2) nanofluid coolant provides more cooling effectiveness compared to other studied coolants (nanofluids and water), for both copper and APG porous matrices for different porosity values. In summary, similar results are observed regarding the effect of porous material, porosity and nanofluids for both square and rectangular cross section channels. Temperature distribution along the transverse direction at the centerline of the base is also studied and compared for different coolants, porous materials, and porosity values (Fig. 8). The results confirm that titanium dioxide (TiO2) nanofluid coolant has more cooling effectiveness compared to other studied coolants (nanofluids and water), for both copper and APG porous matrices for high and low porosity values. In addition, the diamond nanofluid has the lowest thermal effectiveness compared to pure water and all other studied water based nanofluid cool-
ants. Also similar to the results for the rectangular cross sectional inlet cases, APG porous substrates provides a better cooling along the transverse direction compared to that of copper substrate for the same coolant or porosity. In addition, the lower porosity would result in more efficient cooling along the transverse direction but at a greater pressure drop. Studying the effect of inlet cross section, the results indicate larger temperature nonuniformity along the transverse direction for the cases with a square cross section. In addition, larger temperature values are observed in the regions far from the inlet channel (Fig. 8). As such, the cases with square cross section provide lower temperature values along the streamwise direction while result in less uniformity specially along transverse direction. Utilization of APG or low porosity substrates improves cooling effectiveness along the transverse direction.
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6. Conclusions Electronic cooling is one of the main issues in the development of advanced devices such as electronics and biomedical components. In this work, an innovative porous filled heat exchanger is numerically modeled to investigate the thermal performance of different nanofluid coolants, porous materials, porosity values, and inlet channel geometry. The heat exchanger is filled with a highly conductive porous insert providing a large surface area for a given volume to enhance heat transfer and thermal control. Two different porous solid materials (copper and annealed pyrolytic graphite (APG)) with different porosity values, utilizing different nanofluids (5% titanium dioxide (TiO2) in water, 1% alumina in water, 0.03% multi walled carbon nanotubes (MWCNT) in water, and 1% diamond in 40:60 ethylene glycol/water) are investigated. The results indicate the importance of proper selection of the porous medium and the coolant for improving the cooling process. Both copper and APG porous substrates can provide a proper cooling at the base of the heat exchanger with rectangular and square inlet channels. However, utilization of APG porous matrix provides a better cooling at the base leading to lower temperature values. APG is a lighter and more conductive material, but fragile in comparison with copper. The results also show that utilizing titanium dioxide (TiO2) nanofluid as coolant improves cooling efficiency in all cases with rectangular and square cross sectional inlets, copper and APG porous matrices, and low and high porosity values. The effect of inlet channel geometry, square and rectangular, was also investigated. The results indicate a lower temperature distribution along streamwise direction for the cases with square cross sectional inlet, while along the transverse direction higher temperature values are observed far from the center for the square cross section inlet channel.
Conflict of interest There is no conflict of interest. This manuscript has not been submitted to anywhere else.
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